You can
put this solution on YOUR website!Can anyone give me any tips on factoring the greatest common monomial factor
from a polynomial. I dont have a problem to submit. I have a lesson sheet for
my class but the lesson isnt in the text book we use. If anyone can help I
appretiate it.
6x³y - 9x³y²z + 12x²y³z²
We first look for a number we can take out.
6, 9 and 12 can all three be divided evenly
by 3, so we can take out a 3. So far,
GCF = 3....
Now we look at the letter x
6x³y - 9x³y²z + 12x²y³z²
The first term contains x³. The second term
contains x³ and the third term contains x².
Thus x appears in ALL factors so we can
take out the smallest power of x. The
smallest power of x is x², so we can take
out x². So far
GCF = 3x²....
Now we look at the letter y
6x³y - 9x³y²z + 12x²y³z²
The first term contains y or y¹. The second
term contains y² and the third term contains y³.
Thus y appears in ALL factors so we can
take out the smallest power of y. The
smallest power of y is y¹, so we can take
out y¹, or just y. So far
GCF = 3x²y....
Now we look at the letter z
6x³y - 9x³y²z + 12x²y³z²
The first term contains no z. Therefore we
cannot take out any power of z, because to
take out a letter, that letter must appear
in ALL the terms, so the final
GCF is
GCF = 3x²y
Now under the original expression
6x³y - 9x³y²z + 12x²y³z²
We write this GCF and a set of parentheses,
long enough to hold 3 terms.
3x²y( )
We have three blanks to fill.
6x³y - 9x³y²z + 12x²y³z²
3x²y(__ - ____ + ____)
To fill the first blank we ask the question:
What must we multiply 3x²y by to get the
first term 6x²y in the original? The answer
is 2x, because the 3 needs to be multiplied by
2 and the x² needs to be multiplied by x, so
3x²y must by multiplied by 2x to get 6x²y
6x³y - 9x³y²z + 12x²y³z²
3x²y(2x - ____ + _____)
To fill the second blank we ask the question:
What must we multiply 3x²y by to get the
second term 9x³y²z in the original? The
answer is 3x¹y¹z or just 3xyz, because
the 3 needs to be multiplied by 3 and the
x² needs to be multiplied by x¹, or just
x, and we must get the z, so we see that
3x²y must by multiplied by 3xyz to get
9x³y²z.
6x³y - 9x³y²z + 12x²y³z²
3x²y(2x - 3xyz + ____)
To fill the third blank we ask the question:
What must we multiply 3x²y by to get the
third term 12x²y³z² in the original? The
answer is 4y²z², because
the 3 needs to be multiplied by 4. We do
not need any x's. The y needs to be
multiplied by y², and we must get z²,
so we see that 3x²y must by multiplied by
4y²z² to get 12x²y³z²
6x³y - 9x³y²z + 12x²y³z²
3x²y(2x - 3xyz + 4y²z²)
That's the final result.
Edwin
